Plastic modal approximations in analyzing beam-on-beam collisions

Haihui Ruan, T. X. Yu, Y. L. Hua

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


Dynamic behavior of a moving free-free beam striking the tip of a cantilever beam, as a typical example of collision between two deformable structures, is analysed by employing modal approximation techniques. The applicability of both rigid-plastic and elastic-plastic mode approximations is examined in predicting the energy partitioning between the two colliding beams. Three rigid-plastic modes (RP-Modes) are considered and the Lee's functional is applied to select the appropriate mode. It is found that one of the beams would absorb all the initial kinetic energy, unless a higher-order RP-mode is adopted. To incorporate the effect of elastic deformation into the modal solution, an elastic, perfectly plastic mode (EP-Mode) approximation for the same problem is proposed. By replacing each of the plastic hinges in the RP-Mode with a nature hinge and an elastic-plastic rotational spring, the fundamental features of the dynamic elastic-plastic behavior of the two colliding beams are revealed. Both beams participate in energy dissipation, while the structural and geometrical parameters greatly influence the energy partitioning. It is shown from numerical examples that the EP-Mode solution provides a fairly good approximation compared with the RP complete solution and finite element simulation.
Original languageEnglish
Pages (from-to)2937-2956
Number of pages20
JournalInternational Journal of Solids and Structures
Issue number12
Publication statusPublished - 1 Jan 2003
Externally publishedYes


  • Beam-on-beam collision
  • Elastic-plastic mode
  • Energy partitioning
  • Modal approximation
  • Rigid-plastic modes

ASJC Scopus subject areas

  • Modelling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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